# Order of element

• Nov 4th 2009, 04:54 PM
apple2009
Order of element
Let G be a finite group. Prove the order of any element v (which v is an element of G) divides the order |G|of G.
• Nov 4th 2009, 04:59 PM
Drexel28
Quote:

Originally Posted by apple2009
Let G be a finite group. Prove the order of any element v (which v is an element of G) divides the order |G|of G.

Hint: $\langle v\rangle$ is a subgroup of $G$. Now apply Lagrange's theorem.
• Nov 4th 2009, 05:04 PM
apple2009
am I need to prove v is a subgroup of G? and how?
• Nov 4th 2009, 05:10 PM
Drexel28
Quote:

Originally Posted by apple2009
am I need to prove v is a subgroup of G? and how?

You already know that $\langle v\rangle$ is a subgroup of $G$ (or you should). Now use the fact that $|v|=|\langle v\rangle|$ and Lagranges theorem.